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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 94640bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.k2 | 94640bd1 | \([0, 1, 0, 1465, -260792]\) | \(2048/175\) | \(-29692598244400\) | \([2]\) | \(199680\) | \(1.2646\) | \(\Gamma_0(N)\)-optimal |
| 94640.k1 | 94640bd2 | \([0, 1, 0, -53460, -4610852]\) | \(6224272/245\) | \(665114200674560\) | \([2]\) | \(399360\) | \(1.6112\) |
Rank
sage: E.rank()
The elliptic curves in class 94640bd have rank \(1\).
Complex multiplication
The elliptic curves in class 94640bd do not have complex multiplication.Modular form 94640.2.a.bd
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
